GGT und KGV
Author: Mag.G.Wengler

Der rote Punkt kann bewegt werden und liefert Breite und Länge des Rechtecks.
Gibt bei ggT die Seite der größtmöglichen Fliese an, mit der das Rechteck ausgelegt werden kann.

Bewege mich

ggT:

kgV:

z

z

Anzahl der Fliesen:

z

Alles \;richtig!

Fliesen zeigen

A = (30, 56)
A1: x(A)
B1: y(A)
A2 = If(A1 > B1, A1 - B1, A1)
B2 = If(A1 > B1, B1, B1 - A1)
A3 = If(A2 > B2, A2 - B2, A2)
B3 = If(A2 > B2, B2, B2 - A2)
A4 = If(A3 > B3, A3 - B3, A3)
B4 = If(A3 > B3, B3, B3 - A3)
A5 = If(A4 > B4, A4 - B4, A4)
B5 = If(A4 > B4, B4, B4 - A4)
A6 = If(A5 > B5, A5 - B5, A5)
B6 = If(A5 > B5, B5, B5 - A5)
A7 = If(A6 > B6, A6 - B6, A6)
B7 = If(A6 > B6, B6, B6 - A6)
A8 = If(A7 > B7, A7 - B7, A7)
B8 = If(A7 > B7, B7, B7 - A7)
A9 = If(A8 > B8, A8 - B8, A8)
B9 = If(A8 > B8, B8, B8 - A8)
A10 = If(A9 > B9, A9 - B9, A9)
B10 = If(A9 > B9, B9, B9 - A9)
A11 = If(A10 > B10, A10 - B10, A10)
B11 = If(A10 > B10, B10, B10 - A10)
A12 = If(A11 > B11, A11 - B11, A11)
B12 = If(A11 > B11, B11, B11 - A11)
A13 = If(A12 > B12, A12 - B12, A12)
B13 = If(A12 > B12, B12, B12 - A12)
A14 = If(A13 > B13, A13 - B13, A13)
B14 = If(A13 > B13, B13, B13 - A13)
A15 = If(A14 > B14, A14 - B14, A14)
B15 = If(A14 > B14, B14, B14 - A14)
A16 = If(A15 > B15, A15 - B15, A15)
B16 = If(A15 > B15, B15, B15 - A15)
A17 = If(A16 > B16, A16 - B16, A16)
B17 = If(A16 > B16, B16, B16 - A16)
A18 = If(A17 > B17, A17 - B17, A17)
B18 = If(A17 > B17, B17, B17 - A17)
A19 = If(A18 > B18, A18 - B18, A18)
B19 = If(A18 > B18, B18, B18 - A18)
A20 = If(A19 > B19, A19 - B19, A19)
B20 = If(A19 > B19, B19, B19 - A19)
A21 = If(A20 > B20, A20 - B20, A20)
B21 = If(A20 > B20, B20, B20 - A20)
A22 = If(A21 > B21, A21 - B21, A21)
B22 = If(A21 > B21, B21, B21 - A21)
A23 = If(A22 > B22, A22 - B22, A22)
B23 = If(A22 > B22, B22, B22 - A22)
A24 = If(A23 > B23, A23 - B23, A23)
B24 = If(A23 > B23, B23, B23 - A23)
A25 = If(A24 > B24, A24 - B24, A24)
B25 = If(A24 > B24, B24, B24 - A24)
A26 = If(A25 > B25, A25 - B25, A25)
B26 = If(A25 > B25, B25, B25 - A25)
A27 = If(A26 > B26, A26 - B26, A26)
B27 = If(A26 > B26, B26, B26 - A26)
A28 = If(A27 > B27, A27 - B27, A27)
B28 = If(A27 > B27, B27, B27 - A27)
A29 = If(A28 > B28, A28 - B28, A28)
B29 = If(A28 > B28, B28, B28 - A28)
A30 = If(A29 > B29, A29 - B29, A29)
B30 = If(A29 > B29, B29, B29 - A29)
A31 = If(A30 > B30, A30 - B30, A30)
B31 = If(A30 > B30, B30, B30 - A30)
A32 = If(A31 > B31, A31 - B31, A31)
B32 = If(A31 > B31, B31, B31 - A31)
A33 = If(A32 > B32, A32 - B32, A32)
B33 = If(A32 > B32, B32, B32 - A32)
A34 = If(A33 > B33, A33 - B33, A33)
B34 = If(A33 > B33, B33, B33 - A33)
A35 = If(A34 > B34, A34 - B34, A34)
B35 = If(A34 > B34, B34, B34 - A34)
A36 = If(A35 > B35, A35 - B35, A35)
B36 = If(A35 > B35, B35, B35 - A35)
A37 = If(A36 > B36, A36 - B36, A36)
B37 = If(A36 > B36, B36, B36 - A36)
A38 = If(A37 > B37, A37 - B37, A37)
B38 = If(A37 > B37, B37, B37 - A37)
A39 = If(A38 > B38, A38 - B38, A38)
B39 = If(A38 > B38, B38, B38 - A38)
A40 = If(A39 > B39, A39 - B39, A39)
B40 = If(A39 > B39, B39, B39 - A39)
A41 = If(A40 > B40, A40 - B40, A40)
B41 = If(A40 > B40, B40, B40 - A40)
A42 = If(A41 > B41, A41 - B41, A41)
B42 = If(A41 > B41, B41, B41 - A41)
A43 = If(A42 > B42, A42 - B42, A42)
B43 = If(A42 > B42, B42, B42 - A42)
A44 = If(A43 > B43, A43 - B43, A43)
B44 = If(A43 > B43, B43, B43 - A43)
A45 = If(A44 > B44, A44 - B44, A44)
B45 = If(A44 > B44, B44, B44 - A44)
A46 = If(A45 > B45, A45 - B45, A45)
B46 = If(A45 > B45, B45, B45 - A45)
A47 = If(A46 > B46, A46 - B46, A46)
B47 = If(A46 > B46, B46, B46 - A46)
A48 = If(A47 > B47, A47 - B47, A47)
B48 = If(A47 > B47, B47, B47 - A47)
A49 = If(A48 > B48, A48 - B48, A48)
B49 = If(A48 > B48, B48, B48 - A48)
A50 = If(A49 > B49, A49 - B49, A49)
B50 = If(A49 > B49, B49, B49 - A49)
A51 = If(A50 > B50, A50 - B50, A50)
B51 = If(A50 > B50, B50, B50 - A50)
A52 = If(A51 > B51, A51 - B51, A51)
B52 = If(A51 > B51, B51, B51 - A51)
A53 = If(A52 > B52, A52 - B52, A52)
B53 = If(A52 > B52, B52, B52 - A52)
A54 = If(A53 > B53, A53 - B53, A53)
B54 = If(A53 > B53, B53, B53 - A53)
A55 = If(A54 > B54, A54 - B54, A54)
B55 = If(A54 > B54, B54, B54 - A54)
A56 = If(A55 > B55, A55 - B55, A55)
B56 = If(A55 > B55, B55, B55 - A55)
A57 = If(A56 > B56, A56 - B56, A56)
B57 = If(A56 > B56, B56, B56 - A56)
A58 = If(A57 > B57, A57 - B57, A57)
B58 = If(A57 > B57, B57, B57 - A57)
A59 = If(A58 > B58, A58 - B58, A58)
B59 = If(A58 > B58, B58, B58 - A58)
A60 = If(A59 > B59, A59 - B59, A59)
B60 = If(A59 > B59, B59, B59 - A59)
A61 = If(A60 > B60, A60 - B60, A60)
B61 = If(A60 > B60, B60, B60 - A60)
A62 = If(A61 > B61, A61 - B61, A61)
B62 = If(A61 > B61, B61, B61 - A61)
A63 = If(A62 > B62, A62 - B62, A62)
B63 = If(A62 > B62, B62, B62 - A62)
A64 = If(A63 > B63, A63 - B63, A63)
B64 = If(A63 > B63, B63, B63 - A63)
A65 = If(A64 > B64, A64 - B64, A64)
B65 = If(A64 > B64, B64, B64 - A64)
A66 = If(A65 > B65, A65 - B65, A65)
B66 = If(A65 > B65, B65, B65 - A65)
A67 = If(A66 > B66, A66 - B66, A66)
B67 = If(A66 > B66, B66, B66 - A66)
A68 = If(A67 > B67, A67 - B67, A67)
B68 = If(A67 > B67, B67, B67 - A67)
A69 = If(A68 > B68, A68 - B68, A68)
B69 = If(A68 > B68, B68, B68 - A68)
A70 = If(A69 > B69, A69 - B69, A69)
B70 = If(A69 > B69, B69, B69 - A69)
A71 = If(A70 > B70, A70 - B70, A70)
B71 = If(A70 > B70, B70, B70 - A70)
A72 = If(A71 > B71, A71 - B71, A71)
B72 = If(A71 > B71, B71, B71 - A71)
A73 = If(A72 > B72, A72 - B72, A72)
B73 = If(A72 > B72, B72, B72 - A72)
A74 = If(A73 > B73, A73 - B73, A73)
B74 = If(A73 > B73, B73, B73 - A73)
A75 = If(A74 > B74, A74 - B74, A74)
B75 = If(A74 > B74, B74, B74 - A74)
A76 = If(A75 > B75, A75 - B75, A75)
B76 = If(A75 > B75, B75, B75 - A75)
A77 = If(A76 > B76, A76 - B76, A76)
B77 = If(A76 > B76, B76, B76 - A76)
A78 = If(A77 > B77, A77 - B77, A77)
B78 = If(A77 > B77, B77, B77 - A77)
sL = Sequence(Segment[(Cell[1, i], Cell[2, i]), (Cell[1, i], 0)], i, 1, 100)
wL = Sequence(Segment[(Cell[1, i], Cell[2, i]), (0, Cell[2, i])], i, 1, 100)
A79 = If(A78 > B78, A78 - B78, A78)
B79 = If(A78 > B78, B78, B78 - A78)
A80 = If(A79 > B79, A79 - B79, A79)
B80 = If(A79 > B79, B79, B79 - A79)
A81 = If(A80 > B80, A80 - B80, A80)
B81 = If(A80 > B80, B80, B80 - A80)
A82 = If(A81 > B81, A81 - B81, A81)
B82 = If(A81 > B81, B81, B81 - A81)
A83 = If(A82 > B82, A82 - B82, A82)
B83 = If(A82 > B82, B82, B82 - A82)
A84 = If(A83 > B83, A83 - B83, A83)
B84 = If(A83 > B83, B83, B83 - A83)
A85 = If(A84 > B84, A84 - B84, A84)
B85 = If(A84 > B84, B84, B84 - A84)
A86 = If(A85 > B85, A85 - B85, A85)
B86 = If(A85 > B85, B85, B85 - A85)
A87 = If(A86 > B86, A86 - B86, A86)
B87 = If(A86 > B86, B86, B86 - A86)
A88 = If(A87 > B87, A87 - B87, A87)
B88 = If(A87 > B87, B87, B87 - A87)
A89 = If(A88 > B88, A88 - B88, A88)
B89 = If(A88 > B88, B88, B88 - A88)
A90 = If(A89 > B89, A89 - B89, A89)
B90 = If(A89 > B89, B89, B89 - A89)
A91 = If(A90 > B90, A90 - B90, A90)
B91 = If(A90 > B90, B90, B90 - A90)
A92 = If(A91 > B91, A91 - B91, A91)
B92 = If(A91 > B91, B91, B91 - A91)
A93 = If(A92 > B92, A92 - B92, A92)
B93 = If(A92 > B92, B92, B92 - A92)
A94 = If(A93 > B93, A93 - B93, A93)
B94 = If(A93 > B93, B93, B93 - A93)
A95 = If(A94 > B94, A94 - B94, A94)
B95 = If(A94 > B94, B94, B94 - A94)
A96 = If(A95 > B95, A95 - B95, A95)
B96 = If(A95 > B95, B95, B95 - A95)
A97 = If(A96 > B96, A96 - B96, A96)
B97 = If(A96 > B96, B96, B96 - A96)
A98 = If(A97 > B97, A97 - B97, A97)
B98 = If(A97 > B97, B97, B97 - A97)
A99 = If(A98 > B98, A98 - B98, A98)
B99 = If(A98 > B98, B98, B98 - A98)
A100 = If(A99 > B99, A99 - B99, A99)
B100 = If(A99 > B99, B99, B99 - A99)
xL = Sequence(Text[i, (i, -2)], i, 0, x(A), 10)
yL = Sequence(Text[i, (-3, i)], i, 0, y(A), 10)
list3 = Sequence(Ray[(0, i), (1, i)], i, 1, 200)
list4 = Sequence(Ray[(i, 0), (i, 1)], i, 1, 200)
ggt = GCD(A1, B1)
lg: x(A) / ggt
br: y(A) / ggt
Fliesen = Sequence(Sequence[Polygon[(i * ggt, j * ggt), ((i + 1) * ggt, j * ggt), 4], i, 0, lg - 1], j, 0, br - 1)
kgv = LCM(x(A), y(A))
anzahl: kgv / ggt
w_1 = 0
w_2 = 0
w_3 = 0
Textfeld1 = Textfield(w_1)
Textfeld2 = Textfield(w_2)
Textfeld3 = Textfield(w_3)
r_1: w_1 ≟ ggt
r_2: w_2 ≟ kgv
r_3: w_3 ≟ anzahl
a = false
Text6: "" + (LaTeX[x(A)]) + "\  und\ " + (LaTeX[y(A)]) + ""